Explicit expressions of response sensitivities for structural systems subjected to stationary random processes

This paper deals with sensitivity analysis of the stationary stochastic response of linear discretized structures with uncertain stiffness parameters subjected to stationary multi-correlated Gaussian random excitation. Approximate explicit expressions of the sensitivities of the probabilistic characteristics of the response are derived. The proposed procedure relies on the so-called rational series expansion (RSE), recently derived by the authors as an alternative explicit form of the Neumann expansion of the inverse of an invertible matrix with a modification of rank r. For validation purposes, numerical results concerning a wind-excited truss structure with uncertain Young’s moduli have been included in the paper.